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# Category: Sculptures and Models

# G4G9, Day 5: Balancing Laptops, Mobius Music, and Egg Cartons

This is the 6th and final post in a series of posts about Gathering For Gardner: * ** 1 2 3 4 5
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I started the last day of Gathering For Gardner 9 by waking up late.

As a result, I completely missed the first talk and entered the conference room in the middle of the second talk, by Karl Schaffer, about “Dancing Tessellations”. It consisted mainly of a few videos in which a normal dance would be reflected along certain axes so that it effectively makes a video tessellation. The next one was a short talk on extending the Side-Angle-Side (SAS) similarity theorem to three-dimensional shapes using the least possible number of measurements. One of the especially interesting talks in the first session was by Linda Zayas-Palmer, on why the infinite number, 0.999999… , is actually not just equivalent to, but greater than, 1. The talk directly after that was about some of Salvador Dali’s puzzles in some of his paintings, in which you have to find a certain phrase. Turns out his puzzles are rather easy. My favorite talk in the session, though, was by Burkard Polster on how to balance your laptop on a bedside table such that it occupies the minimum amount of space on the table and doesn’t fall off. It starts out by a simple dissection of a square by Martin Gardner, and then exteds it to show how to balance the laptop *just right* so that it’ll balance, thus leaving room for puzzles or whatever you would put on a bedside table.

During the break, Mom and I went up to the exhibit room, where the exhibitors were packing up their exhibits. Most of the exhibits were already gone, but a few were there that weren’t the first time. For one of these, involving curious polyhedral sculptures made with egg cartons, Mom actually got to talk with Jeannie Mosely, the person who made them. In fact, she actually got a model of the octahedron which had fairly novel methods of holding together as an example to make more.

After the break, the talks continued with a talk on 3-dimensional packing puzzles made out of various spheres glued together to make polyomino-like shapes. Due to the spherical nature of the pieces, some of the puzzles need the polyspheres to “snap” together, something which doesn’t normally happen. A rather good talk in this session was by Ed Pegg, about the Wolfram Demonstrations Project, and some of the best demonstrations that had been posted, such as a program to find the smallest box that squares of size 1/n can fit in:

Or even how to solve the Orchard-Planting Problem, involving finding a certain number of lines that pass through a certain number of points, given the required points:

The talk after Ed Pegg’s talk was one of the most anticipated talks of the entire conference: Finding a single shape that covers the entire plane aperiodically, which was an unsolved problem. Joshua Socolar managed to find a single hexagonal tile (with matching rules, though) which creates a Sierpinski Gasket-like shape when made. He also made a 3-dimensional tile which acts the same.

Afterwards, Vi Hart did a great talk on making music with music boxes with the music scores in Mobius strips, or the music boxes arranged in such a way so that the music played by one music box is played by another music box seconds later.

After Vi Hart’s talk the lunch break started, but instead of going to lunch I went immediately up to the Gift Exchange area, where I would wait in line to get a bag full of exchange gifts from nearly everybody, repeated for everyone, who would get one also.

Apparently everybody else had the same idea of waiting in line early. I ended up behind Bram Cohen, inventor of BitTorrent as well as a whole bunch of super-duper-hard twisty puzzles which have some rather ingenious ideas behind them. He happened to have a few non-twisty, but still hard, puzzles while waiting in line, and I managed to *almost* solve one of them (the Cast Rattle), which involved getting the right pieces in the right place (That isn’t a spoiler, is it?). The other one, Cast Marble, I couldn’t get immediately, but I might have been getting close. Soon, I got to the front of the line to get my bag of exchange gifts and got the huge bag (I could barely carry it) as well as a few other miscellaneous items from people at a few nearby tables, such as a perplexing wooden object which looked like a gear, or a few pictures from Caspar Schwabe (I presume) of large inflatable solids, including the huge 59th stellation of the icosahedron seen on day 3.

I brought the huge bag of gifts up to the hotel room to open, and even though the bag’s heaviness was an indicator of the number of things inside, it still felt like Christmas when I opened it. There were mathematical dice with the sides only using the number nine and a set of plastic rings with interchangeable art based on the Traveling Salesman problem; there was a CD containing rather high-quality pictures as well as a digital copy of the exchange book from G4G8; A set of pieces for an unsolved puzzle and a key to open doors with using a hammer; A book about formulae that changed the world and a second copy of A New Kind of Science(Ah, so *that’s* where the heaviness came from);Even a mysterious back-scratcher and tapper. These are just a few of the things in the bag, and to list them all out would certainly lengthen this blog post by quite a lot.

By the time I had gotten to the bottom of the bag, the third session was about to start so I had to rush down to see the talk by Gordon Hamilton (of the Magical Mathematics Museum) about having problems in K-12 classrooms involving unsolved problems such as the circle-packing problem (In how small a square can you pack n circles?), the 3n+1 conjecture (Do all Collatz sequences end in 4,2,1?), and others. Also in the same session was Solomon Golomb’s talk about the Pentomino Game on nxn boards. The “Pentomino Game”, is a rather interesting two-player game in which players alternate turns placing pentominoes onto an 8×8 board. The first player who can not place another piece loses. One of the most interesting talks of the session was “Fun with Egg Cartons” by Jeannie Mosely. In the talk, she described how she made most of the Platonic Solids – out of egg cartons! The process of making these is pretty easy- just interleave strips of egg cartons at the vertices to make the edges- but the results are still interesting.

Immediately following was a talk not relating to mathematics at all (but still cool), about restoring various ancient text adventures. The talk was by Adam Atkinson, and it was about cross-compiling old text adventures (running on mainframes) so that you could play them on newer computers. Many of them are stored at ifarchive.org (the Archive for Interactive Fiction), including Acheton, probably the third text adventure ever made. Just don’t get eaten by a grue.

After the last short break, the last session of G4G9 began. Kate Jones started of with a philosophical talk involving pentomino puzzles,followed by Bill Mullins, who talked about Martin Gardner’s search for the person who wrote “The Expert at the Card Table”, probably the most important book ever on sleight of hand with cards, who wrote his name as “S.W.Erdnase”. It can be reversed to make E.S.Andrews , but from there it’s much harder. So far, they’ve found 5 suspects as to who S.W.Erdnase might be, 2 by Gardner and 3 by others, but the writer remains hidden. Hirokazu Iwasawa (also known as Iwahiro) then followed that with a talk about the subclass of “Hat-Team Puzzles” , how to solve them, as well as other variations on the problem. A bit later, Colin Wright did a double talk about “How far is the Moon?” and about notations for juggling. The former was left out (the pdf is available here) , but the talk about juggling was amazing. Not only did he juggle normally with up to 5 balls, but he also showed how to use a notation for juggling to make up your own tricks, some insanely complex and others trivial. Following that, George Hart talked about his new sculpture, “Comet!” which involves multiple smaller versions of the main model (a puzzle-like polyhedral-ish form) with different colors. It’s so big that it has to be hung on the ceiling of an atrium. After that, Mike Keith did the second-to-last talk about his book, Not A Wake, in which every word of the text- including the subtitle and the title- has the same number of letters as the nth digit of pi does. The book goes on for 10,000 digits, with 10 stories followed by the digits of pi in that story, each story being a different style than the others.

After the last talk and closing notes, G4G9 was over. However, the fun(at least for me) continued. I was invited to dinner (along with Bill Gosper, Mom, Julian and Corey Hunts) by Dick Esterle to the Varsity Jr., an old-style fast food diner that had been operating for 45 years. Bill and Julian declined, but the rest of us went.

The diner had good food (especially the burgers) , and talking with Esterle was quite interesting. I brought a box puzzle (the same from the prelude) , and he managed to solve it in record time just by shaking it hard. He also, using the materials that were available, gave me 2 versions of the same puzzle. First, arrange 3 cups in an equilateral triangle such that a knife can reach from any cup to any other cup. Then, use the knives to balance a salt shaker in the middle of the triangle above the table. (This can be done using 2 knives) Then, set the cups so that they are just a bit too far for the knives to reach, and once again balance the salt shaker using 3 knives. Corey and I eventually solved it and put a few straw decorations on (from my solution to the problem using straws to extend the knives and only using 2 knives). To prevent spoilers, it’s at http://daftmusings.stattenfield.org/wp-content/uploads/2010/04/Neil-and-Corey-at-the-Varsity-copy.jpg .

After dinner, Dick Esterle drove us back to the Ritz-Carlton, where we went back up to our hotel rooms and played with puzzles until bedtime.

The day after that, I was waken up very early to get packed up for the airplane trip back to San Jose. We met Bill Gosper in the hotel lobby, and took a cab to the airport, at which point we waited until dawn-ish. On the airplane trip back (with an exchange in Chicago), I looked at all of the exchange gifts in the bag and Bill Gosper programmed on his laptop. Eventually, after having 2 breakfasts due to time zones, we landed in San Jose, drove over to my house, whereupon Bill drove back to his house. And because of time zones, I still had the rest of the day to play with puzzles.

Thus the epic of Gathering for Gardner 9 ended.

It was an absolutely great experience from before it even started to it’s end, and I met a lot of new people and saw a lot of puzzles and magic tricks and optical illusions. I would certainly go the next time it happens, and the time after that. Certainly, it was one of the best events that I attended ever, if not the best.

As an afterword, on May 22, Martin Gardner died. Hearing the news of this was incredibly saddening to me, as well as sudden. He was one of the most important people that ever lived, for mathematics and as well as for many other subjects. He helped popularize M.C. Escher and *Godel,Escher,Bach* , and introduced mathematics in a fun way to at least everybody at any of the G4Gs. He was truly amazing.

# G4G9, Day 4: Lasers, Sculptures, and Balloon Polyhedra

This is the 5th post in a series of posts about Gathering For Gardner: * ** 1 2 3 4*

We woke up the next day, and soon realized that the first talk had already started, but only by around a minute. Luckily, the conference was in the hotel I was staying in, so I only arrived a few minutes late. The first talk was by Jean Pedersen, about the extended face planes of various polyhedra. The next few talks were rather interesting: Zdravko Zivkovic introduced a puzzle called “MemorIQ” where you have to make various shapes out of octagonal pieces which are colored on the sides. The sides of the pieces touching must also be the same, so it is a bit of a challenge to make a square with the pieces. Al Seckel then did a talk on “The Nature of Belief”, talking about various ambiguous optical illusions which change completely when you add a simple line to them, as well as a music track reversed which originally sounds like gibberish, but when words are added, comes out very clear. Greg Federickson did a talk on “Symmetry vs. Economy in Dissections of Squares and Cubes”. In it, he showed many demonstrations of dissecting squares and cubes into many smaller squares and cubes, in very symmetrical ways and also in the minimum number of pieces. He also showed examples for *hinged* dissections, some of which were very ingenious, especially for the cubes. Lastly, Robert Crease talked about his new book about some of the most important equations in mathematics and science.

After a short break, the 2nd session began. Pablos Holman stated out with a great talk about “Hackers and Invention” in which he demonstrated how to kill mosquitoes by shooting lasers, changed the voicemail sound on Al Seckel’s phone by spoofing his caller ID, displayed a robot that wheels up to people and shows them their passwords, and showed how to pick a lock very quickly using a filed-down key and a hammer. After this talk, I went out with Bill Gosper, who was going to show John Conway the Universal Game Of Life Computer which Calcyman had made computing Pi. Bill also showed Conway some other Game of Life patterns, such as the same universal computer computing the digits of the Golden Ratio, and a Python script for going to a particular step in a Life simulation faster than the normal algorithm, which he demonstrated by simulating a pattern to a googol-1 steps. Because of this, I was a bit late for the last talk of the day, the overview of the math sculptures that were to be made later that day at Tom Rodger’s house, which ranged from a button knot to a huge zonohedral pavilion.

I had a quick lunch (i.e, none) and boarded the bus that would be going to Tom’s house. On the way there, I tried to figure out some particularly hard puzzles which had little or no instructions, and also talked with some of the other attendees. When we arrived, they had a lot of Japanese-style lunches set out on a table for us to eat before building the various sculptures and seeing some of the things that were already set up. Some of the most interesting things there were a metal polyhedral-ish sculpture that George Hart was making, an impossible box that you could stand in, and a huge black hyperbola that towered over everything else.

After eating my lunch, I helped build the base for the zonohedral pavilion by soaping the pieces and then placing them into place on the supports. When that was done, they started on the roof of the pavillion, and I showed a few puzzles to other attendees, inlcuding a version of the Enigma puzzle as well as a “chopstick” puzzle using some of the left-over chopsticks from lunch.

Afterwards , I helped out on another sculpture, this time a metal sculpture of a three-dimensional Peano curve, which had to be put together using near-identical pieces and screws. The pieces were very rusty, so my hands got very dirty. Eventually it was almost done and I wandered off somewhere else. Back near the house, Vi Hart had been showing people how to make various polyhedra out of balloons, such as simple octahedra and cubes.

I went with Gareth Conway and Max to explore a section of the landscape which Max said was an entrance to a gold or a silver mine, and which was almost completely covered with leaves from the surrounding trees. At some point, Max said that we’ll get famous for discovering this gold mine, to which Gareth responded that he was already famous for that he knew 130 digits of pi. I promptly responded with all of the digits of Pi I knew (only 30), and Gareth corrected me when I added on a few extra digits. It’s good that Michael Keith, the author of a book entirely written in Pilish wasn’t there at that point, because then I’d have to listen to quite a lot of digits of Pi. Eventually, however, it turned out that the “gold mine” was actually just a well.

Meanwhile, the polyhedral balloon-making had gotten completely out of control:

I went back to the main area, where I saw that a lot of the sculptures had been finished, such as the Chinese Button Knot and George Hart’s sculpture. I got to talk with Clifford Pickover about various things, such as the non-paradox that 100% of all integers have a 9 in them, and about some of the artwork in *The Math Book*, Pickover’s new book. Nearby was Ivan Moscovich, whom I talked with as well about various puzzles, such as his Mirrorkal series of sliding block puzzles in which you have to make a certain image with the pieces, which have mirrors on them so that the first puzzle is figuring out what configuration the blocks should be in afterwards. Soon, nearly all of the sculptures had been finished except for the pavilion which was almost finished and it was getting dark.

We had quite a nice dinner, although the tables were full so I had to sit nearby, where Gosper was. We talked for some time, and I mentioned a formula that can calculate Pi to 42 billion digits but then soon diverges. After the dinner, I went into Tom’s house which, as I have said before, is absolutely filled with puzzles. I played with a few puzzles, including a 3-piece burr and a few Japanese puzzle boxes but then encountered a puzzle that fell apart and then was impossible to put back together. By that time, it was time to go back to the hotel. I boarded the bus in the back- right next to George Hart and a few other people who had made the sculptures at Tom’s house that day, who I talked with for the ride back.

It had been a great day, and there was only 1 day of the conference left.